A guide to the Choquard equation

Moroz, Vitaly;Van Schaftingen, Jean
(2017) Journal of Fixed Point Theory and Applications — Vol. 19, n° 1, p. 773-813 (2016)

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Abstract
We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations −Δu+V(x)u=(|x|−(N−α)∗|u|p)|u|p−2u in RN, and some of its variants and extensions.
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Moroz, V., & Van Schaftingen, J. (2017). A guide to the Choquard equation. Journal of Fixed Point Theory and Applications, 19(1), 773-813. https://doi.org/10.1007/s11784-016-0373-1 (Original work published 2016)